You were correct, no need for the entire 'lifestory' type call. Again no strict need for the frequency but in your scenario it's possibly of help to enable the ATCO to check that you had changed (the respective frequency being transmitted on normally has a light indication when active on the controllers desk / console).
Of course, the big clue here is the word 'contact' - the person taking control already has all your details and so doesn't need to hear them all again.
CM